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Golden ratio

Source: 2024 CTST P8

March 11, 2024
geometryratio

Problem Statement

In △ABC\triangle {ABC}, tangents of the circumcircle ⊙O\odot {O} at B,CB, C and at A,BA, B intersects at X,YX, Y respectively. AXAX cuts BCBC at D{D} and CYCY cuts ABAB at F{F}. Ray DFDF cuts arc ABAB of the circumcircle at P{P}. Q,RQ, R are on segments AB,ACAB, AC such that P,Q,RP, Q, R are collinear and QR∥BOQR \parallel BO. If PQ2=PR⋅QRPQ^2=PR \cdot QR, find ∠ACB\angle ACB.
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